A249153 Exponent of 2 in the hyperfactorial of 2n: a(n) = A007814(A002109(2n)).

0, 2, 10, 16, 40, 50, 74, 88, 152, 170, 210, 232, 304, 330, 386, 416, 576, 610, 682, 720, 840, 882, 970, 1016, 1208, 1258, 1362, 1416, 1584, 1642, 1762, 1824, 2208, 2274, 2410, 2480, 2696, 2770, 2922, 3000, 3320, 3402, 3570, 3656, 3920, 4010, 4194, 4288, 4768, 4866, 5066, 5168, 5480, 5586, 5802, 5912

Offset: 0

Author

Antti Karttunen, Oct 25 2014

Keywords

• nonn

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..10000

Crossrefs

Bisection of A249152.

Cf. A002109, A007814, A143157, A069895 (first differences).

Programs

Mathematica

Table[IntegerExponent[Hyperfactorial[2*n], 2], {n, 0, 55}] (* Amiram Eldar, Sep 10 2024 *)

Python

from sympy import multiplicity
A249153_list, n = [0], 0
for i in range(2,20002,2):
    n += multiplicity(2,i)*i
    A249153_list.append(n) # Chai Wah Wu, Aug 21 2015

Formula

a(n) = A249152(2*n) = A007814(A002109(2*n)).

a(n) = 2*A143157(n).

a(n) ~ 2*n^2. - Amiram Eldar, Sep 10 2024